Answer:
Linear equation with a slope of 2 that goes through the point (3, 4) is [tex]y = 2\cdot x -2[/tex].
Step-by-step explanation:
From statement we know the slope of the line and a point contained in it. Using the slope-point equation of the line is the quickest approach to determine the appropriate equation, whose expression is:
[tex]y-y_{o} = m \cdot (x-x_{o})[/tex]
Where:
[tex]m[/tex] - Slope, dimensionless.
[tex]x_{o}[/tex], [tex]y_{o}[/tex] - Components of given point, dimensionless.
[tex]x[/tex], [tex]y[/tex] - Independent and dependent variable, dimensionless.
If we know that [tex]m = 2[/tex], [tex]x_{o} = 3[/tex] and [tex]y_{o} = 4[/tex], the linear equation is found after algebraic handling:
1) [tex]y-4 = 2\cdot (x-3)[/tex] Given
2) [tex]y = 2\cdot (x-3) +4[/tex] Compatibility with Addition/Existence of Additive Inverse/Modulative Property
3) [tex]y = 2\cdot x -2[/tex] Distributive Property/[tex](-a)\cdot b = -a\cdot b[/tex]/Definition of sum/Result
Linear equation with a slope of 2 that goes through the point (3, 4) is [tex]y = 2\cdot x -2[/tex].
